有限光滑性条件下的一致平稳相位估计
Uniform stationary phase estimate with limited smoothness
AI总结：
本文利用波包分解将振荡积分衰减估计转化为波包支集的几何不交性，显著降低了 Alazard-Burq-Zuily 一致平稳相位估计所需的正则性。
摘要：
本文研究带平稳相位的振荡积分的一致估计，该问题此前由 Alazard-Burq-Zuily 研究过。我们显著降低了该一致估计对相位函数和振幅函数所需正则性条件的阶数。我们还研究了相位函数和振幅函数依赖于振荡参数的振荡积分的估计。本文的新颖之处在于使用波包分解，将振荡积分的衰减估计转化为波包支集的不交性性质。后者本质上是几何性的，对相位函数和振幅函数的光滑性较不敏感。
英文摘要：
In this paper, we consider the uniform estimate for the oscillatory integral with stationary phase, which was previously studied by Alazard-Burq-Zuily. We significantly reduce the order of required regularity condition on the phase and amplitude functions for the uniform estimate. We also study estimates for the oscillatory integrals of which phase and amplitude functions depend on the oscillation parameter. The novelty of this article lies in the use of the wave packet decomposition, which transforms the decay estimate for the oscillatory integral to the disjointness property of the supports of wave packets. The latter is geometric in its nature and less sensitive to the smoothness of the phase and amplitude functions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
